
Samsung Galaxy Tab Pro 8.4
The latest firmware for Samsung Galaxy Tab Pro 8.4 (SM-T320NU) is T320NUUEU1AOB8 with Android 4.4.2 (KitKat), released on February 23, 2015 for 1 region (CSC). Every official firmware build for SM-T320NU, newest first: one row per build with all regions (CSC) that received it.
Each firmware build has its own page at https://samfirm.shop/build/{PDA}, where {PDA} is the build number from the list above. Example: https://samfirm.shop/build/T320NUUEU1AOB8
Specifications of SM-T320N, a regional variant of the same device. Chipset and SIM lines are left out: they can differ by region.

SM-T320X

SM-T321

SM-T310X

SM-T330X

SM-T337V
You can find the firmware on the model: SM-T320NU page.
Yes, all firmware files for SM-T320NU are 100% official, original, and obtained directly from Samsung servers.
To flash SM-T320NU, you need to download the appropriate firmware, put your device into Download Mode, and use the Odin tool to load the BL, AP, CP, and CSC files.
Downgrading is only possible if the bootloader version (binary bit) of the old firmware matches the current one. Always check the binary version before flashing SM-T320NU.